Computer-based geospatial applications typically allow a user to associate an event with a discrete geographic location on the surface of a planetary body such as the Earth. This process of associating events with geographic locations is commonly referred to as “geotagging”. For example, a series of crime incidents may be each be associated with a geographic coordinate to indicate where the crime incidents occurred. As another example, the population count of a town may be associated with a geographic coordinate to indicate the population at a particular geographic location.
In addition to functionality for geotagging, geospatial applications may also include functionality for density mapping. Very generally, density mapping includes distributing a geotagged event over a geographic area and displaying a surface (“density surface”) on a two-dimensional planar map to give a visual indication of the density of the geotagged event as distributed over the geographic area. For example, a geospatial application may generate a heat map to indicate a density of crime incidents in a city. The areas of conceptually hotter colors on the heat map represent areas of high event density (e.g., areas of higher incidences of criminal activity) while areas of conceptually cooler colors represent areas of lower event density (e.g., areas of lower incidences of criminal activity).
Various approaches may be used to display a density surface on a planar map. For example, according to a planar distance-based approach, distances in a two-dimensional planar coordinate system are used to determine how density is distributed over a geographic area displayed on the map. One problem with the planar distance-based approach is that it does not account for projection distortions in the map on which the density surface is displayed. Projection distortions result from “flattening” the curved surface of a planetary body into a plane to be displayed as a map. Projection distortions include distortions of one or more of shape, area, distance, and direction. Projection distortions are generally more pronounced over large geographic areas such as, for example, in maps of the whole Earth.
As an example of distortions caused by “flattening” a curved surface into a plane, a Mercator map projection, which is commonly used to create a map of the surface of the Earth, produces a map in which both area and distance are distorted with the greatest distortions near the North and South Poles. For example, in a Mercator map of the whole Earth, Greenland is presented as having roughly the same geographic surface area as the continent of Africa. However, in actuality, Africa's surface area is many times the size of Greenland's surface area.
With the planar distance-based approach, density surfaces are generated irrespective of the projection distortions of the map on which the density surfaces are displayed. For example, if there are two density surfaces, one near the North Pole and the other near the Equator, using the planar distance-based approach on a Mercator projected map would result in two identical appearing density surfaces (i.e., same area, shape, size, and falloff) being displayed on the map even though geographic areas near the North Pole would have greater projection distortions than the area near the Equator. Thus, the planar distance-based approach may produce a density surface with a significantly inaccurate representation of the geographic area covered by the density surface and a significantly inaccurate representation of density falloff over the covered geographic area.
As users of geospatial applications become more sophisticated, the need for greater accuracy in density mapping has increased. Consequently, there is a need to be able to more accurately present the geographic area covered by a density surface when the density surface is displayed on a map, especially when the density surface is displayed on a map that represents a large geographic area such as a map of the whole Earth. Similarly, there is a need to be able to more accurately represent density falloff over the covered geographic area.
The approaches described in this section are approaches that could be pursued, but not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any of the approaches described in this section qualify as prior art merely by virtue of their inclusion in this section.